Fisher Score Matching for ΛCDM Neural Network-Assisted

Cosmological parameter inference of the ΛCDM model (Ωm, σ8) combining three key components: a neural network that learns the Fisher score function (TensorFlow/Keras), the physical emulator CAMB for the power spectrum P(k), and MCMC for posterior Bayesian inference.

Final project for Machine Learning in Cosmology (Master's in Physics). Author: José Ake · github.com/ak3sit0 Method based on Sui et al. (2025), Fisher Score Matching.

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Idea

Given a real parameter θ = (Ωm, σ8), its physical observable P(k) is generated with CAMB and a noisy version θ* = θ + ε, ε ~ N(0, σ²). The network learns to map the spectrum to the noisy parameter, approximating the Fisher score function that guides sampling via Langevin/MCMC toward the posterior. The result is contrasted against a reference MCMC.

Pipeline

1. Simulation (CAMB): synthetic dataset (θ, θ*, P(k)).
2. Training: neural network (Keras) that estimates Fisher score.
3. Inference: MCMC sampling guided by the network.
4. Validation: comparison of posteriors (corner plots) against standard MCMC.

Results

Dataset P(k)	Training History	Comparative Posterior

Reproduce

pip install -r requirements.txt
jupyter notebook notebooks/score_matching_lcdm.ipynb

The trained model (models/modelo_score.keras) and normalizers (models/normalizers.json) are included to reproduce inference without re-training. The data/ folder is generated when running the simulation phase with CAMB.

Structure

cosmology-score-matching/
├── notebooks/   score_matching_lcdm.ipynb   # complete pipeline
├── models/      modelo_score.keras · normalizers.json
├── figures/     results
├── report/      final report (PDF)
└── presentation/

Stack

camb · tensorflow / keras · numpy · matplotlib · seaborn · corner

License

Code under MIT license. © 2026 José Ake.

Reference

• Sui et al. (2025), Fisher Score Matching for Simulation-Based Inference.